Design: Cluster RCT, with 3 levels, and randomization done at level 3 (district level).

Models: random treatment effects.

Power Validation

Default parameters:

  • M = 3
  • J = 40
  • K = 20
  • rho: \(\rho\) = 0.5
  • ATE ES = 0.25, 0.25, 0.25
  • R2: \(R^2_1\) = 0.1, 0.1, 0.1, \(R^2_2\) = 0.1, 0.1, 0.1, \(R^2_3\) = 0.1, 0.1, 0.1
  • ICC: \(\text{ICC}_2\) = 0.1, 0.1, 0.1, \(\text{ICC}_3\) = 0.1, 0.1, 0.1
  • Omega: \(\omega_2\) = 0, \(\omega_3\) = 0

Base case

Varying school size

\(\bar{n}\) = 100

\(\bar{n}\) = 75

Varying R2

\(R^2_1 =\) 0.6, 0.6, 0.6

\(R^2_2 =\) 0.6, 0.6, 0.6

\(R^2_3 =\) 0.6, 0.6, 0.6

\(R^2_1 =\) 0, 0, 0 \(R^2_2 =\) 0, 0, 0 \(R^2_3 =\) 0, 0, 0

Varying rho

\(\rho =\) 0.2

\(\rho =\) 0.8

Varying true positives

ATE (ES) = 0.25, 0, 0

Varying ICC

\(\text{ICC}_2\) = 0.7, 0.7, 0.7

\(\text{ICC}_3\) = 0.7, 0.7, 0.7

\(\text{ICC}_2\) = 0, 0, 0

\(\text{ICC}_3\) = 0, 0, 0

Kappa

\(\kappa\) = 0.4

MDES validation

## 
## 
## +------------+---------------+---------------+-------------+
## |    MTP     | Adjusted MDES | D1indiv Power | Target MDES |
## +============+===============+===============+=============+
## |    rawp    |    0.1767     |    0.2141     |    0.25     |
## +------------+---------------+---------------+-------------+
## | Bonferroni |    0.2509     |    0.2141     |    0.25     |
## +------------+---------------+---------------+-------------+
## |     BH     |    0.2522     |    0.3036     |    0.25     |
## +------------+---------------+---------------+-------------+
## |    Holm    |    0.2513     |    0.2615     |    0.25     |
## +------------+---------------+---------------+-------------+
## 
## Table: d3.3_m3rc2rc

Sample size validation

## 
## 
## +------+-------------+-------------+---------------+
## | MTP  | Sample type | Sample size | D1indiv power |
## +======+=============+=============+===============+
## |  BH  |      J      |    3267     |     0.308     |
## +------+-------------+-------------+---------------+
## | Holm |      J      |    2587     |    0.2636     |
## +------+-------------+-------------+---------------+
## 
## Table: d3.3_m3rc2rc
## 
## 
## +------+-------------+-------------+---------------+
## | MTP  | Sample type | Sample size | D1indiv power |
## +======+=============+=============+===============+
## |  BH  |      K      |     20      |    0.2983     |
## +------+-------------+-------------+---------------+
## | Holm |      K      |     21      |    0.2585     |
## +------+-------------+-------------+---------------+
## 
## Table: d3.3_m3rc2rc
## 
## 
## +------+-------------+-------------+---------------+
## | MTP  | Sample type | Sample size | D1indiv power |
## +======+=============+=============+===============+
## |  BH  |    nbar     |    3227     |    0.3014     |
## +------+-------------+-------------+---------------+
## | Holm |    nbar     |    7238     |    0.2592     |
## +------+-------------+-------------+---------------+
## 
## Table: d3.3_m3rc2rc